Shioda-Tate formula for an abelian fibered variety and applications

Details Shioda-Tate formula for an abelian fibered variety and applications Shioda-Tate formula for an abelian fibered variety and applications

2007-03-09

arxiv.org/abs/math/0703245v1

Mathematics

Algebraic Geometry

10 pages

Scientific paper

We give an explicit formula for the Mordell-Weil rank of an abelian fibered
variety and some of its applications for an abelian fibered hyperk\"ahler
manifold. As a byproduct, we also give an explicit example of an abelian
fibered variety in which the Picard number of the generic fiber in the sense of
scheme is different from the Picard number of generic closed fibers.

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